We present the systematic results for three dimensional fragmentation functions of spin one hadrons defined via quark-quark correlator. There are totally 72 such fragmentation functions, among them 18 are twist-2, 36 are twist-3 and 18 are twist-4. We also present the relationships between the twist-3 parts and those defined via quark-gluon-quark correlator obtained from the QCD equation of motion. We show that two particle semi-inclusive hadron production process e + e − → VπX at high energies is one of the best places to study the three-dimensional tensor polarization dependent fragmentation functions. We present the general kinematic analysis of this process and show that the cross section should be expressed in terms of 81 independent structure functions. After that we present parton model results for the hadronic tensor, the structure functions, the azimuthal and spin asymmetries in terms of these gauge invariant fragmentation functions at the leading order pQCD up to twist-3.
The longitudinal polarization of hyperon in e + e − annihilation at high energies depends on the longitudinal polarization of the quark produced at the e + e − annihilation vertex whereas the spin alignment of vector mesons is independent of it. They exhibit very different energy dependences. We use the longitudinal polarization of Lambda hyperon and the spin alignment of K * as representative examples to present numerical results of energy dependences and demonstrate such distinct differences. We present the results at the leading twist with perturbative QCD evolutions of fragmentation functions at the leading order.
We present the complete twist-4 results for the semi-inclusive annihilation process e + + e − → h +q + X at the tree level of perturbative quantum chromodynamics. The calculations are carried out by using the formalism obtained by applying the collinear expansion to this process where the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. We present the results for structure functions in terms of gauge invariant fragmentation functions up to twist-4 and the corresponding results for the azimuthal asymmetries and polarizations of hadrons produced. The results obtained show in particular that similar to that for semi-inclusive deeply inelastic scattering, for structure functions associated with sine or cosine of odd number of azimuthal angle(s), there are only twist-3 contributions, while for those of even number of azimuthal angle(s), there are leading twist and twist-4 contributions. For all those structure functions that have leading twist contributions, there are twist-4 addenda to them. Hence twist-4 contributions may even have large influences on extracting leading twist fragmentation functions from the data. We also suggest a method for a rough estimation of twist-4 contributions based on the leading twist fragmentation functions.
We present the systematic results for three dimensional fragmentation functions defined via the quark-quark correlator for hadrons with spin 0, 1/2 and 1 respectively. These results are presented in terms of a spin independent part, a vector polarization dependent part and a tensor polarization dependent part. For spin 0 hadrons, only the spin independent part is needed, for spin 1/2 hadron, the polarization independent and vector polarization dependent parts are present, while for spin 1 hadrons, all the three parts exist. We discuss the general properties of these fragmentation functions and also present the corresponding results when transverse momentum is integrated.
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